Weight-strength optimization of wooden household chairs based on member section size

Abstract

Weight-strength optimization of wooden household chairs was performed based on the member section size in this study. Member section sizes of the Scotch pine (Pinus sylvestris) and Oriental beech (Fagus orientalis) chairs were optimized and resulting re-manufactured optimized chairs were tested under the cyclic "front to back", "back to front" and "backrest" loads according to American Library Association (ALA) specification. Finite element method (FEM) and MATLAB nonlinear programming were utilized for the optimization. Firstly, the internal forces and moments acting on each member were analyzed by FEM in order to obtain the maximum critical stresses in each type of member; then, optimized cross-sectional sizes of the members were determined by Gradient Descent method, and all constraints were treated with Logarithmic Barrier Functioning. As a result, the minimum section sizes of members were determined, and cyclic performance tests were performed to determine whether the optimized chairs were strong enough to carry the acceptable loads. According to the results, member section size of both beech and pine chairs could be significantly reduced. The reduction was 32 % in the total weight and volume for beech chairs while 16 % for pine chairs without sacrificing the performance required for domestic usage by ALA. In conclusion, the method used is suitable for the optimization of furniture frames, making it lighter and reducing the material costs.